Modulus Definition and 583 Threads

how do we take derivative of modulus of a function??

Homework Statement Let f be an analytic function on the disc |z|<1 and satisfies |f(z)|≤M if |z|<1. Show that |f(z)| \le M \left| \frac{z-a}{1-a'z} \right| when |z|<1 where a' is the complex conjugate of a Homework Equations This section uses maximum modulus principle, but I really don't...

Homework Statement In a project in a summer engineering class I'm taking, I have been tasked with finding Young's Modulus with three different diameters of spaghetti: Thin (1.41 mm), Normal (1.73 mm), and Thick (1.89 mm). Although this is my first time ever attempting to try engineering...

I have a screw that is used in our plant that is rated to break at 39 ft/lbs of torque. The diameter of the shaft is .130 inches. What is the shear modulus of the material that is being used. Thanks

Homework Statement From A.P. French, question 3-10. I'm having trouble decoding part b. /Do not solve/ please help me find what it is asking. ------- A metal rod, 0.5m long, has a rectangular cross section of 2mm2. (a) This question provided me with information to calculate young's modulus...

What is the threshold where Young's modulus stops being applicable, and ultimate strength becomes relevant?

Homework Statement This is from A.P. French, Vibrations and Waves, Problem 3-7 A wire of unstretched length l0 is extended by a distance of 10-3l0 when a certain mass is hung from its bottom end. If this same wire is [turned to be horizontal] and the same mass is hung from the midpoint of...

I appreciate your help with this problem from a Three point Bending Test in Wood samples Homework Statement Force: 2400 N Deflection: 4.3 mm Span: 343 mm Length: 392 mm b: 24.01 mm d: 24.25 MOE: 16445.15 MPa How can I calculate the Modulus of Elasticity with shear corrected...

Can anyone help me understand this questions from 800score.com ? I'm finding it hard to understand the modulus function Solve 14 - 9|x - 8| = 15 Kindly review this question and help me out on this as my exams are nearing. Thank You.

Homework Statement Prove that if gcd(a, 133) = 1, then 133 divides (a^18 - 1). The Attempt at a Solution This is an old homework question as I'm going over the homeworks to review for the test, but can't seem to get this right. Which is annoying because I remember I did it fine back in the...

How can I get Young's modulus value of Ferrous Tungsten? Is it possible to get it from Young's modulus value of Ferrous and Young's modulus value of Tungsten?

Homework Statement I want to know the Young's Modulus of Ferrous Tungsten. Homework Equations Is it possible to get the Young's modulus of ferrous Tungsten from Young's modulus of ferrous and Young's modulus of Tungsten? The Attempt at a Solution

Q. Show that the area between the positive x-axis, the y-axis and the curve y = ||e^x - 1| - 1| is ln4 - 1 I've drawn the curve: http://gyazo.com/cfd52af0f82e0e7d6b063681a73de45a I notice for x < 0 (as I drew e^x to start out with, that's how I noticed it): y = e^xfor x>ln(2) y = e^x - 2...

I've got a beam of Length 500mm under third point loading. width = 100mm depth=100mm Force at rupture is 6.627kN change in length =0.000019m = 0.019mm can someone help me with the Youngs modulus please i'm getting 6.87 GPa... which seems a bit low for concrete? Although possible...

Hi guys, I've been trying to help a friend with something that I learned in class but I'm now finding it hard to solve myself. The problem goes as follows: Use geometry to show that |z3-z-3| = 2sin3θ For z=cisθ, 0<θ<∏/6 Now, I chose ∏/12 as my angle and plotted all this on an Argand diagram...

Hello! I am looking for a catalog that contains redshift, modulus distance and position (if it is possible) of many type Ia supernovae as possible. I have found this: http://www.cbat.eps.harvard.edu/lists/Supernovae.html, but this link only has the position data. Does anyone know wher I...

Homework Statement An Aluminum cable of length 3.5m has 15,000 N tensile force acting on it if the wire is only allowed to be stretched by 1mm before it breaks, What must be the radius of the wire if the Young's modulus of Al is 6.9 x 10^10 N/m^2? I am also supposed to find the tensile...

I'm dealing with a cylinder. The equation for the stress of each is Force / Area. What are the different areas for the equation in regard to young's modulus, bulk modulus, and shear modulus? Is the area Young's Modulus stress the area of circle face? What about for shear stress? Would the...

Solve for x: 4x=6(mod 5) Here is my solution: From the definition of modulus, we can write the above as \frac{4x−6}{5}=k, where k is the remainder resulting from 4x~mod~5=6~mod~5=k. Solving for x, x=\frac{5k+6}{4}⟹x(k)=\frac{5k+6}{4} Now, my teacher said that is incorrect, and that...

Homework Statement This is a rather conceptual question, but is there a difference between elasticity and young's modulus? I know that the young's modulus can also be stated as the modulus of elasticity, but is it incorrect to say that a substance with a higher young's modulus has a low...

Young's Modulus of Elasticity Problems - URGENT Homework Statement Calculate Young's Modulus of Elasticity for the three materials using the graphs only. Stress (N/m2) Strain 70 0.06 100 0.11 150 0.22 200 0.35 220...

After a fall, a 77 kg rock climber finds himself dangling from the end of a rope that had been 15 m long and 9.1 mm in diameter but has stretched by 2.3 cm. For the rope, calculate (a) the strain, (b) the stress, and (c) the Young's modulus. strain = ΔL/L stress = F/A Young's modulus =...

Does a single crystal specimen have a smaller Young's Modulus than a polycrystalline specimen? I think a single crystal would have a lower elastic mudolus since it has less grain boundaries and probably less dislocations than a polycrystalline specimen. I'd appreciate any ideas thanks

Why is it: $$ \langle A \rangle = \int dV ~ \psi^* (\hat{A} \psi) $$ As opposed to: $$ \langle A \rangle = \int dV ~ (\hat{A} \psi^*) (\hat{A} \psi) $$ The op can substantially change the wf, so it would seem to make more mathematical sense (at least from a linear algebra pov) to...

Could somebody please tell me if we can apply young modulus theory to a slinky spring, or can only be applied to a rod when strenched?If possible to apply to the slinky spring, how can we calculate the elasticity of that slinky spring?by the way what is the process by which slinky springs are...

If a shear force is acting on a rectangular beam, how do I use the value of the shear modulus to calculate if the force applied will fracture the beam? Below I've submitted the data involved. The shear force applied is 1000 N and the cross section area is 28 mm. So the shear force applied is...

It is generally well known that the elastic modulus of most materials become larger with decreasing size. This could be due to decreased number of dislocations, surface effects etc. Does anyone know how exactly does this increase? Considering a ceramic or an oxide, how does the Elastic modulus E...

Quoted from my book: "The graph of ΔL against F has gradient L/EA, so the Young modulus E is equal to L(A x gradient)." E is (stress/strain). I don't understand that sentence. If I substitute the gradient into E= L(A x gradient), then E= L(A)(L/EA) E= L(L/E) E= L^2 /E E square = L square...

Question 1: --> Why both the wires are suspended from the same rigid support in this experiment? Question 2: -->Why both the wires are taken of the same material?

The figure shows an aluminum wire of length L 1 = 60.0 cm, cross-sectional area 1.00 x 10-2 cm2, and density 2600 kg/m3, joined to a steel wire of density 7.80 g/cm3 and the same cross-sectional area. The compound wire, loaded with a block of mass 10.0 kg, is arranged so that the distance L...

What is |exp (z^n)| less than if |z| < 1? I'm thinking it's e but I'm having a brain freeze at the moment! Thanks for any help guys.

I have a question wondering if you guys could check over for me . I have a solution no sure on its accuracy! the question is in two parts a bar has a 25mm diameter and is subjected to a tensile force of 61Kn, the extension on a gauge length of 50mm is 0.1mm. calculate the youngs modulus in...

Even though this deals with programming an encryption algorithm I feel this is more math based so I'm asking it here. x=((y mod 380951)*3182) mod 380951 How can I solve for y? A few helpful points: 1) the math involved here is limited to integers, so for example division by 3182 must...

Hey guys, I'm doing some experimenting recently with some primality tests, and I need help figuring out how to automate the following: Given an even number N, divide by 2k (k \in \mathbb{N}). If N/2k is an integer, reduce mod 2k+1. (If N/2k is not an integer, simply move on to the next one.)...

The engineering yield strength, the modulus of elasticity, the original diameter and final diameter of a wire are given. That wire is stretched and it diameter decreases. I am trying to find the engineering strain just before yield and the corresponding true strain. So I assume I will find...

A hanging wire made of an alloy of titanium with diameter 0.14 cm is initially 2.9 m long. When a 97 kg mass is hung from it, the wire stretches an amount 1.49 cm. A mole of titanium has a mass of 48 grams, and its density is 4.54 g/cm3. Based on these experimental measurements, what is...

Homework Statement How to calculate the modulus of elasticity algebraically? Especially that of a pine wood rectangular cantilever beam? I have a few measurements here. The area inertia is .413 cm^4, the length of the unsupported part of the beam is at 40 centimeters(the whole beam is around 66...

We know that the Young's modulus of an object is defined as the ratio between its stress and strain: Y = σ/ε , or: Y = F*L/A*ΔL We also know that Hooke's law, which can be applied to any linear elastic object, can find spring constant: F = k*x , rearranged: k = F/x But is...

Homework Statement I've been asked to find the stiffness constant of a rubber band and young's modulus. To do this I created the experiment like this http://www.gcsesciencemethods.co.uk/2012/05/hookes-law-1.html and then i put all the values in a table. I plotted a graph of extension vs weight...

Homework Statement A extremely strong wire of exotic material has a radius of 0.1 mm and a length of 5 m. A 1000 kg mass is hung vertically from the wire. The speed of sound in the wire is observed to be the same as the speed of a transverse wave on the wire. What is the Bulk Modulus of the...

Mechanical principles - Stress and modulus of elasticity Homework Statement A 2.2m long steel towing bar of solid circular section diameter of 45mm is expected to carry a maximum load of 210 kN. The safety factor is 4; and for the steel the UTS is 540 MNm-2 and the modulus of elasticity is...

I did a practical worked the gradient and calculated E, of a wooden metre rule. What I want is a value to compare my value with, I got 5 N/m2 So 5N will bend the ruler 1m? Seems likely right?

Does |\psi(\mathbf{x},t)|^2d^3\mathbf{x} or |\psi(\mathbf{x},t)|^2d^3\mathbf{x}dt give the probability of a particle to collapse at the point \mathbf{x} at time t? Griffiths sides with the former, but I'm having doubts.

Question #1) In a new bungee sport a 70 kg rider is projected from the shore, out into a lake for a splash with a human scale slingshot. The stretched slingshot is made with a set of 50 cylindrical rubber tubes 1) stretched at a 45 degree angle from the horizontal. The tubes are cylindrical...

Here goes try number two, the forum deleted my last post. :cry: First time poster, so hopefully I'm following the rules, I do apologise if I'm not. I have a problem with my lab report, I would be very grateful if anyone could help. Thanks. Homework Statement I'm writing a tensile test lab...

Homework Statement In Figure, a 103 kg uniform log hangs by two steel wires, A and B, both of radiuses 1.20 mm. Initially, wire A was 2.50 m long and 2.00 mm shorter than wire B. The log is now horizontal. What are the magnitudes of the forces on it from Wire A, and Wire B? Ysteel= 2.00*10^(11)...

(This is my first post.) I can't seem to find a good way of solving this sort of congruence for x: x^2 / 3 + 11 \equiv 5 (mod x) Through trial and error it appears at least 3 and 6 are answers, but how can you reach them regularly? (I'm heard conflicting things about fractions being...

I am feeling silly because I can't seem to crack this, but maybe I have been staring at it too long. I am trying to find a math function that will yield a single unit decrement of the currently defined Year/Quarter. This is a software UI thing: I am trying to create a script to decrement, in...

Homework Statement If I said minimize the cost function |a-2b| + |-3a-b| subject to 2a + b <= 6 a,b >= 0 We can all see it's 0,0 but if I want to apply the simplex algorithm to it, how do I reformulate the problem into something I can use Homework Equations The Attempt at...

Homework Statement A liquid is enclosed in a metal container that is provided with a piston of the same metal. The system is originally at a pressure of 1.00 atm (1.013*10^5 Pa) and at a temperature of 30.0 C. The piston is forced down until the pressure on the liquid is increased by 50.0 atm...